On Efficient Spatial Matching

This paper proposes and solves a new problem called spatial matching (SPM). Let P and O be two sets of objects in an arbitrary metric space, where object distances are defined according to a norm satisfying the triangle inequality. Each object in O represents a customer, and each object in P indicates a service provider, which has a capacity corresponding to the maximum number of customers that can be supported by the provider. SPM assigns each customer to her/his nearest provider, among all the providers whose capacities have not been exhausted in serving other closer customers. We elaborate the applications where SPM is useful, and develop algorithms that settle this problem with a linear number O(|P | + |O|) of nearest neighbor queries. We verify our theoretical findings with extensive experiments, and show that the proposed solutions outperform alternative methods by a factor of orders of magnitude.